It is exhibited that mature scientific economical theory is a set of propositions that describe the relationship between theoretical objects of two types - basic objects and derivative ones. The set of basic objects makes up the aggregate of initial idealizations (the Fundamental Theoretical Scheme or FTS) with no direct reference to experimental data. The derivative theoretical objects are formed from the basic ones according to certain rules. The sets of derivative objects form partial theoretical schemes or PTS. Any (...) mature economics scientific theory grows due to transitions, in order to describe each new experimental situation, from FTS to PTS. Each PTS construction from the FTS represents a problem that cannot be reduced to a strict algorithm. (shrink)

In this paper I elicit a prediction from structural realism and compare it, not to a historical case, but to a contemporary scientific theory. If structural realism is correct, then we should expect physics to develop theories that fail to provide an ontology of the sort sought by traditional realists. If structure alone is responsible for instrumental success, we should expect surplus ontology to be eliminated. Quantum field theory (QFT) provides the framework for some of the best (...) confirmed theories in science, but debates over its ontology are vexed. Rather than taking a stand on these matters, the structural realist can embrace QFT as an example of just the kind of theory SR should lead us to expect. Yet, it is not clear that QFT meets the structuralist's positive expectation by providing a structure for the world. In particular, the problem of unitarily inequivalent representations threatens to undermine the possibility of QFT providing a unique structure for the world. In response to this problem, I suggest that the structuralist should endorse pluralism about structure. (shrink)

This paper argues that the theory of structured propositions is not undermined by the Russell-Myhill paradox. I develop a theory of structured propositions in which the Russell-Myhill paradox doesn't arise: the theory does not involve ramification or compromises to the underlying logic, but rather rejects common assumptions, encoded in the notation of the $\lambda$-calculus, about what properties and relations can be built. I argue that the structuralist had independent reasons to reject these underlying assumptions. The theory (...) is given both a diagrammatic representation, and a logical representation in a novel language. In the latter half of the paper I turn to some technical questions concerning the treatment of quantification, and demonstrate various equivalences between the diagrammatic and logical representations, and a fragment of the $\lambda$-calculus. (shrink)

While structural equations modeling is increasingly used in philosophical theorizing about causation, it remains unclear what it takes for a particular structural equations model to be correct. To the extent that this issue has been addressed, the consensus appears to be that it takes a certain family of causal counterfactuals being true. I argue that this account faces difficulties in securing the independent manipulability of the structural determination relations represented in a correct structural equations model. I then offer an alternate (...) understanding of structural determination, and I demonstrate that this theory guarantees that structural determination relations are independently manipulable. The account provides a straightforward way of understanding hypothetical interventions, as well as a criterion for distinguishing hypothetical changes in the values of variables which constitute interventions from those which do not. It additionally affords a semantics for causal counterfactual conditionals which is able to yield a clean solution to a problem case for the standard ‘closest possible world’ semantics. (shrink)

The theory of mind debate has reached a “hybrid consensus” concerning the status of theory-theory and simulation-theory. Extant hybrid models either specify co-dependency and implementation relations, or distribute mentalizing tasks according to folk-psychological categories. By relying on a non-developmental framework these models fail to capture the central connection between simulation and theory. I propose a “dynamic” hybrid that is informed by recent work on the nature of similarity cognition. I claim that Gentner’s model of (...) class='Hi'>structure-mapping allows us to understand simulation as a process in which psychological representations are aligned, causing the spontaneous abstraction of theoretical generalizations about the psychological domain. (shrink)

We model scientific theories as Bayesian networks. Nodes carry credences and function as abstract representations of propositions within the structure. Directed links carry conditional probabilities and represent connections between those propositions. Updating is Bayesian across the network as a whole. The impact of evidence at one point within a scientific theory can have a very different impact on the network than does evidence of the same strength at a different point. A Bayesian model allows us to envisage and (...) analyze the differential impact of evidence and credence change at different points within a single network and across different theoretical structures. (shrink)

Alasia Nuti’s recent book Injustice and the Reproduction of History: Structural Inequalities, Gender and Redress puts forward a compelling vision of contemporary duties to redress past wrongdoing, grounded in the idea of “historical-structural-injustice”, constituted by the “structural reproduction of an unjust history over time and through changes”. Such an approach promises to transcend the familiar scholarly divide between “backward-looking” and “forward-looking” models, and allow for a reparative approach that focuses specifically on those past wrongs that impact the present, while retaining (...) a significant focus on the historical. While Nuti’s work is perhaps the most sophisticated treatment of structural injustice to date, this paper argues that an exclusive concentration on historical-structural-injustices neglects some aspects and some acts of wrongdoing that call out for present-day redress. What is needed, therefore, is a pluralist theory that can accept the pressing force in the present of historical-structural-injustices, whilst also making room for past-regarding duties that either do not fit, or are not best conceptualized in terms of, this approach, without being overwhelmed by the sheer scale of historic injustice. (shrink)

Physical theories are complex and necessary tools for gaining new knowledge about their areas of application. A distinction is made between abstract and practical theories. The last are constantly being improved in the cognitive activity of professional physicists and studied by future physicists. A variant of the philosophy of physics based on a modified structural-nominative reconstruction of practical theories is proposed. Readers should decide whether this option is useful for their understanding of the philosophy of physics, as well as other (...) philosophies of particular sciences. (shrink)

This unpublished paper, written in 2005 in the PhD philosophy program at Notre Dame, argues that algebraic structural realism faces a difficulty raised by the existence of inequivalent representations in quantum field theory.

Lukács is widely recognized as being the first critical theorist to have explicitly developed the idea of a “standpoint theory”. According to such a theory, members of oppressed groups enjoy an epistemic privilege regarding the nature of their oppression. However, there is no agreement regarding what precise argument Lukács offers for his claims regarding the alleged epistemic privilege of the working class. Additionally, it remains unclear whether later feminist standpoint theories share any continuity with Lukács’s argument. In this (...) analysis, I identify four arguments for the epistemic privilege of oppressed groups that could be attributed to Lukács. I argue that, although Lukács does not consistently endorse any specific argument, the most promising interpretation suggests that epistemic privilege arises from a contradiction between the norms that guide the self-understanding of such groups and the effects of the social practices they are socially obligated to engage in. (shrink)

Structural analogies connect Williamson’s epistemology and action theory: for example, action is the direction-of-fit mirror image of knowledge, and knowledge stands to belief as action stands to intention. These structural analogies, for Williamson, are meant to illuminate more generally how ‘mirrors’ reversing direction of fit should be understood as connecting the spectrum of our cognitive and practically oriented mental states. This paper has two central aims, one negative and the other positive. The negative aim is to highlight some intractable (...) problems with Williamson’s preferred analogical picture, which links the cognitive and the practical through the nexus of direction-of-fit mirroring. The positive aim of the paper is to propose a better alternative. In particular, we show that an achievement-theoretic proposal captures what is in common across the range of attitudes that exhibit the kind of structure that knowledge-belief, action-desire/intention do, while at the same time avoiding the problems shown to face Williamson’s proposed picture. Moreover, we draw attention to several key theoretical benefits of embracing our proposed achievement-theoretic picture, including some of the key benefits of the knowledge-first programme that Williamson’s own analogies were designed to secure. (shrink)

For a long time it was believed that it was impossible to be realist about quantum mechanics. It took quite a while for the researchers in the foundations of physics, beginning with John Stuart Bell [Bell 1987], to convince others that such an alleged impossibility had no foundation. Nowadays there are several quantum theories that can be interpreted realistically, among which Bohmian mechanics, the GRW theory, and the many-worlds theory. The debate, though, is far from being over: in (...) what respect should we be realist regarding these theories? Two diff erent proposals have been made: on the one hand, there are those who insist on a direct ontological interpretation of the wave function as representing physical bodies, and on the other hand there are those who claim that quantum mechanics is not really about the wave function. In this paper we will present and discuss one proposal of the latter kind that focuses on the notion of primitive ontology. (shrink)

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully (...) interrelates a `structural' perspective to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure. (shrink)

Bernard Lonergan has argued for a theory of cognition that is transcendentally secure, that is, one such that any plausible attempt to refute it must presuppose its correctness, and one that also grounds a correct metaphysics and ontology. His proposal combines an identity theory of knowledge with an intentional relation between knower and known. It depends in a crucial way upon an appropriation of one’s own cognitional motives and acts, that is, upon “knowing one’s own knowing.” I argue (...) that because of conflicts between the identity and intentionality components of the theory, rational self-appropriation cannot, as Lonergan claims, be an iteration of just the same acts by which we acquire other sorts of knowledge. I propose an amended theory in which the relation between intending-subject and intended-object of first-level cognition becomes, in RSA, a numerical identity of knower and known and of the epistemic and the ontological. (shrink)

Decision-making under normative uncertainty requires an agent to aggregate the assessments of options given by rival normative theories into a single assessment that tells her what to do in light of her uncertainty. But what if the assessments of rival theories differ not just in their content but in their structure -- e.g., some are merely ordinal while others are cardinal? This paper describes and evaluates three general approaches to this "problem of structural diversity": structural enrichment, structural depletion, and (...) multi-stage aggregation. All three approaches have notable drawbacks, but I tentatively defend multi-stage aggregation as least bad of the three. (shrink)

1Department of Philosophy, University of Nottingham, University Park, Nottingham NG7 2RD, UK. [email protected] of Philosophy, University of Nottingham, University Park, Nottingham NG7 2RD, UK. [email protected].

In this paper we present a new framework of idealization in biology. We characterize idealizations as a network of counterfactual and hypothetical conditionals that can exhibit different “degrees of contingency”. We use this idea to say that, in departing more or less from the actual world, idealizations can serve numerous epistemic, methodological or heuristic purposes within scientific research. We defend that, in part, this structure explains why idealizations, despite being deformations of reality, are so successful in scientific practice. For (...) illustrative purposes, we provide an example from population genetics, the Wright-Fisher Model. (shrink)

Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off (...) between expressive power and meta-theoretic properties when comparing first-order and second-order logic. (shrink)

A discussion of Wolfgang's Stegmüller's ideas on the structuralist conception of theories, especially as presented in his book The Structure and Dynamics of Theories (Springer, 1976).

(v.3) In this paper it is argued that Barad's Agential Realism, an approach to quantum mechanics originating in the philosophy of Niels Bohr, can be the basis of a 'theory of everything' consistent with a proposal of Wheeler that 'observer-participancy is the foundation of everything'. On the one hand, agential realism can be grounded in models of self- organisation such as the hypercycles of Eigen, while on the other agential realism, by virtue of the 'discursive practices' that constitute one (...) aspect of the theory, implies the possibility of the generation of physical phenomena through acts of specification originating at a more fundamental level. This kind of order stems from the association of persisting structures with special mechanisms for sustaining such structures. Included in phenomena that may be generated by these mechanisms are the origin and evolution of life, and human capacities such as mathematical and musical intuition. (shrink)

This thesis considers the following problem: What methods should the epistemology of science use to gain insight into the structure and behaviour of scientific knowledge and method in actual scientific practice? After arguing that the elucidation of epistemological and methodological phenomena in science requires a method that is rooted in formal methods, I consider two alternative methods for epistemology of science. One approach is the classical approaches of the syntactic and semantic views of theories. I show that typical approaches (...) of this sort are inadequate and inaccurate in their representation of scientific knowledge by showing how they fail to account for and misrepresent important epistemological structure and behaviour in science. The other method for epistemology of science I consider is modeled on the methods used to construct valid models of natural phenomena in applied mathematics. This new epistemological method is itself a modeling method that is developed through the detailed consideration of two main examples of theory application in science: double pendulum systems and the modeling of near-Earth objects to compute probability of future Earth impact. I show that not only does this new method accurately represent actual methods used to apply theories in applied mathematics, it also reveals interesting structural and behavioural patterns in the application process and gives insight into what underlies the stability of methods of application. I therefore conclude that for epistemology of science to develop fully as a scientific discipline it must use methods from applied mathematics, not only methods from pure mathematics and metamathematics as traditional formal epistemology of science has done. (shrink)

Types are fundamental for conceptual modeling and knowledge representation, being an essential construct in all major modeling languages in these fields. Despite that, from an ontological and cognitive point of view, there has been a lack of theoretical support for precisely defining a consensual view on types. As a consequence, there has been a lack of precise methodological support for users when choosing the best way to model general terms representing types that appear in a domain, and for building sound (...) taxonomic structures involving them. For over a decade now, a community of researchers has contributed to the development of the Unified Foundational Ontology (UFO) - aimed at providing foundations for all major conceptual modeling constructs. At the core of this enterprise, there has been a theory of types specially designed to address these issues. This theory is ontologically well- founded, psychologically informed, and formally characterized. These results have led to the development of a Conceptual Modelling language dubbed OntoUML, reflecting the ontological micro-theories comprising UFO. Over the years, UFO and OntoUML have been successfully employed on conceptual model design in a variety of domains including academic, industrial, and governmental settings. These experiences exposed improvement opportunities for both the OntoUML language and its underlying theory, UFO. In this paper, we revise the theory of types in UFO in response to empirical evidence. The new version of this theory shows that many of OntoUML’s meta-types (e.g. kind, role, phase, mixin) should be considered not as restricted to substantial types but instead should be applied to model endurant types in general, including relator types, quality types, and mode types. We also contribute with a formal characterization of this fragment of the theory, which is then used to advance a new metamodel for OntoUML (termed OntoUML 2). To demonstrate that the benefits of this approach are extended beyond OntoUML, the proposed formal theory is then employed to support the definition of UFO-based lightweight Semantic Web ontologies with ontological constraint checking in OWL. Additionally, we report on empirical evidence from the literature, mainly from cognitive psychology but also from linguistics, supporting some of the key claims made by this theory. Finally, we propose a computational support for this updated metamodel. (shrink)

Among the possible options for the origin of the universe the most sensible one is nothingness, because it is without a need for any other beginning. It must be possible for nothingness to have a structure so that we can speak about it. The structure of nothingness can be constructed by using inward-outward vanishing points, with a guiding principle of conservation of nothingness. When taken all at once, the inward-outward vanishing points remain as they are—nothing; but when they (...) are taken step-by-step, they become something. The idea of a step-by-step move introduces the idea of time. So time is the first one to emerge as a real-worldly concept from the reading of the structure of nothingness. The Emergence of time gives rise to other real-worldly concepts. What we consider as inward-outward vanishing in the realm of nothingness can now be taken as a turn-by-turn state of expansion and contraction in terms of real world perspectives. And what makes such dynamics possible can be considered as energy. And what has been labelled as conservation of nothingness can now be taken as conservation of energy. And the span of events that emerge due to the introduction of time gives us space. And in space matter is produced. The emergence of matter has only been alluded in the paper, but the possible ingredients and their possible combinations are partially manifested in the field diagrams that are integral parts of the paper, and are also thought to be suitable to the task of mathematization of the metaphysical ideas of the work. (shrink)

Review of: Marinus Dirk Stafleu. Theories at Work: On the Structure and Functioning of Theories in Science, in Particular during the Copernican Revolution. (Christian Studies Today.) 310 pp., bibl., index. Lanham, Md./New York: University Press of America, 1987; Toronto: Institute for Christian Studies, 1987. $28.75 (cloth); $16.50 (paper).

Hiromatsu Wataru’s philosophical thought revolves around an analysis of what he calls the “fourfold structure.” According to Hiromatsu, all phenomena in the world are structured in such a fourfold manner that “a given presents itself as something to someone as Someone,” and these four moments of the phenomenon are not independent elements, but exist only as terms of the functional relationship. This paper surveys and critically examines this theory of the fourfold structure, and shows, in particular, how (...) this theory, while largely presented as synchronic structural analysis, contains some conceptual motifs going beyond the synchronic framework. Specifically, with a focus on the process in which there arises a meaning common to different phenomenal givens and to different knowers, my analysis suggests the way in which phenomena are dynamically structured and thereby displaced in meaning as well as in the knowers’ role relationship. (shrink)

What does it look like when a group of scientists set out to re-envision an entire field of biology in symbolic and formal terms? I analyze the founding and articulation of Numerical Taxonomy between 1950 and 1970, the period when it set out a radical new approach to classification and founded a tradition of mathematics in systematic biology. I argue that introducing mathematics in a comprehensive way also requires re-organizing the daily work of scientists in the field. Numerical taxonomists sought (...) to establish a mathematical method for classification that was universal to every type of organism, and I argue this intrinsically implicated them in a qualitative re-organization of the work of all systematists. I also discuss how Numerical Taxonomy’s re-organization of practice became entrenched across systematic biology even as opposing schools produced their own competing mathematical methods. In this way, the structure of the work process became more fundamental than the methodological theories that motivated it. (shrink)

I reply to criticisms from King and Soames and critically examine two aspects of current orthodoxy about propositions: that they are representational and that they are structured. I argue that (especially once one gives up on intrinsically representational propositions) there is no good reason to think that propositions have representational properties, and distinguish a few different senses in which propositions might be structured, expressing some skepticism about the more ambitious ones.

Epistemic defeat is standardly understood in either evidentialist or responsibilist terms. The seminal treatment of defeat is an evidentialist one, due to John Pollock, who famously distinguishes between undercutting and rebutting defeaters. More recently, an orthogonal distinction due to Jennifer Lackey has become widely endorsed, between so-called doxastic (or psychological) and normative defeaters. We think that neither doxastic nor normative defeaters, as Lackey understands them, exist. Both of Lackey’s categories of defeat derive from implausible assumptions about epistemic responsibility. Although Pollock’s (...) evidentialist view is superior, the evidentialism per se can be purged from it, leaving a general structure of defeat that can be incorporated in a reliabilist theory that is neither evidentialist nor responsibilist in any way. (shrink)

1971. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value, Journal of Structural Learning 3, #2, 1–16. REPRINTED 1976. Structural Learning II Issues and Approaches, ed. J. Scandura, Gordon & Breach Science Publishers, New York, MR56#15263. -/- This is the second of a series of three articles dealing with application of linguistics and logic to the study of mathematical reasoning, especially in the setting of a concern for (...) improvement of mathematical education. The present article presupposes the previous one. Herein we develop our ideas of the purposes of a theory of proof and the criterion of success to be applied to such theories. In addition we speculate at length concerning the specific kinds of uses to which a successful theory of proof may be put vis-a-vis improvement of various aspects of mathematical education. The final article will deal with the construction of such a theory. The 1st is the 1971. Discourse Grammars and the Structure of Mathematical Reasoning I: Mathematical Reasoning and Stratification of Language, Journal of Structural Learning 3, #1, 55–74. https://www.academia.edu/s/fb081b1886?source=link . (shrink)

Clarence I. Lewis (1883-1964) delineated the structure of mind based on his “conceptual pragmatism.” Human mind grounds itself on the ongoing dynamic interaction of relational processes, which is essentially mediated and structural. Lewis’s pragmatism anchors itself on the theory of knowledge that has the triadic structure of the given or immediate data, interpretation, and the concept. Lewis takes the a priori given as a starting point of meaningful experience. The interpretative work of mind is the mediator of (...) the a priori given and the concepts. The a priori given is the principle that determines the application of concepts in our interpretative process. Our mind interprets the given in relating to other possible experience. In other words, the meaning of the a priori given is determined by mind, the subject of interpretative process, which performs constructive and legislative activity, and allows room for the existence of alternatives. Lewis’s theory of knowledge calls for pragmatic justification of value experience. In his ethical theory, Lewis pursues to find answers for how to build up the objectivity of value experience regarding the work of mind as conceptual apparatus. For Lewis, knowledge is a claim about valuation and normativity. In our value experience, the normative significance of our empirical assessments for action comprises objective significance for future experience. Mind is “principle- content apparatus” composed of imperatives as the a priori given principles and the contents of experience as a whole.Imperatives are the result of lessons accumulated from the past and function as rules for the future. Individuals start their experience from imperatives and organize their own experience by doing based on the inferential process, which is directional from the past to the future. (shrink)

When examining the human being as a conscious being, we are still to arrive at an understanding of, firstly, the conditions required whereby physical processes give rise to consciousness and secondly, how consciousness is something fundamental to life as an intrinsic part of nature. Humans are complex organisms with myriad interacting systems whereby the convergence of the activities toward the support and development of the whole organism requires a high level of organisation. Though what accounts for the dynamic unity of (...) the human being? From an empirical perspective the question remains unanswered. The aim of this paper is to conceptually establish a fundamental biophysical organising principle to account for the unity and organisation of the human being. To this end I draw from David Bohm’s interpretation of quantum theory to provide an adapted and adjunct conceptual scheme in the form of a Triple-Aspect-Theory (TAT) of Being as a grounding ontology. David Bohm presented a holistic view of two interwoven orders of existence defined as the Explicate material world and the Implicate (quantum) enfolded world from which the former materialises. Consistent with David Bohm’s idea that matter at a fundamental level consists of a kind of protointelligence, the TAT facilitates a perspective based on aspect conditions of the human organism intended to furnish an explanation of the constitutive mechanism (TAT) inherent in the evolving human being. The TAT operates as an organising principle by which evolution inherently proceeds and maintains itself in an interactive relation between the Implicate and Explicate orders. The accumulated effect of natural selection is to produce adaptations, but without an organising principle: ‘Consciousness’, ‘Body-of-Experience’ and ‘Intellect-Reflective’ (the terms for the engaged coexistent aspects of being) it is argued could not occur. (shrink)

Decision theory has at its core a set of mathematical theorems that connect rational preferences to functions with certain structural properties. The components of these theorems, as well as their bearing on questions surrounding rationality, can be interpreted in a variety of ways. Philosophy’s current interest in decision theory represents a convergence of two very different lines of thought, one concerned with the question of how one ought to act, and the other concerned with the question of what (...) action consists in and what it reveals about the actor’s mental states. As a result, the theory has come to have two different uses in philosophy, which we might call the normative use and the interpretive use. It also has a related use that is largely within the domain of psychology, the descriptive use. This essay examines the historical development of decision theory and its uses; the relationship between the norm of decision theory and the notion of rationality; and the interdependence of the uses of decision theory. (shrink)

This paper presents a simple pair of first-order theories that are not definitionally (nor Morita) equivalent, yet are mutually conservatively translatable and mutually 'surjectively' translatable. We use these results to clarify the overall geography of standards of equivalence and to show that the structural commitments that theories make behave in a more subtle manner than has been recognized.

ABSTRACT This part of the series has a dual purpose. In the first place we will discuss two kinds of theories of proof. The first kind will be called a theory of linear proof. The second has been called a theory of suppositional proof. The term "natural deduction" has often and correctly been used to refer to the second kind of theory, but I shall not do so here because many of the theories so-called are not of (...) the second kind--they must be thought of either as disguised linear theories or theories of a third kind (see postscript below). The second purpose of this part is 25 to develop some of the main ideas needed in constructing a comprehensive theory of proof. The reason for choosing the linear and suppositional theories for this purpose is because the linear theory includes only rules of a very simple nature, and the suppositional theory can be seen as the result of making the linear theory more comprehensive. CORRECTION: At the time these articles were written the word ‘proof’ especially in the phrase ‘proof from hypotheses’ was widely used to refer to what were earlier and are now called deductions. I ask your forgiveness. I have forgiven Church and Henkin who misled me. (shrink)

This paper explores the individualism-holism debate in social ontology and proposes a novel approach to the formalization of our intuitions and claims about social entities. Responding to recent calls for gradualist approaches in lieu of traditional sum-zero scenarios, it is argued that formal tools can be extracted from Integrated Information Theory (IIT) that provide a suitable logical language for gradualist descriptions and analyses of social entities.

This article argues for basic similarities between folkloric and literary narratives. It deals with the relation between narrative structure and the constituent sentences of the narrative text and proposes an adaptation of Hjelmslev's notion of connotative semiotics to account for this. It also draws upon philosophy of action and Austin's 'A Plea for Excuses'.

This paper develops a theory of analog representation. We first argue that the mark of the analog is to be found in the nature of a representational system’s interpretation function, rather than in its vehicles or contents alone. We then develop the rulebound structure theory of analog representation, according to which analog systems are those that use interpretive rules to map syntactic structural features onto semantic structural features. The theory involves three degree-theoretic measures that capture three (...) independent ways in which a system can be more or less analog. We explain how our theory improves upon prior accounts of analog representation, provides plausible diagnoses for novel challenge cases, extends to hybrid systems that are partially analog and partially symbolic, and accounts for some of the advantages and disadvantages of representing analogically versus symbolically. (shrink)

This article applies Charles W. Mills’ notion of the domination contract to develop a Kantian theory of justice. The concept of domination underlying the domination contract is best understood as structural domination, which unjustifiably authorizes institutions and labour practices to weaken vulnerable groups’ public standing as free, equal and independent citizens. Though Kant’s theory of justice captures why structural domination of any kind contradicts the requirements of justice, it neglects to condemn exploitive gender- and race-based labour relations. Because (...) the ideal of civic equality must position all persons as co-legislators of the terms of political rule, the state must dismantle exploitive race- and gender-based labour relations for all persons to command political power as civic equals. (shrink)

A dynamical system is called chaotic if small changes to its initial conditions can create large changes in its behavior. By analogy, we call a dynamical system structurally chaotic if small changes to the equations describing the evolution of the system produce large changes in its behavior. Although there are many definitions of “chaos,” there are few mathematically precise candidate definitions of “structural chaos.” I propose a definition, and I explain two new theorems that show that a set of models (...) is structurally chaotic if it contains a chaotic function. I conclude by discussing the relationship between structural chaos and structural stability. (shrink)

This dissertation examines the theory of perceptual cognition laid out by the 7th century Buddhist scholar, Dharmakīrti, in his magnum opus, the Pramāṇavārttika. Like most theories of perception, both ancient and modern, the sensory cognition of ordinary objects is a topic of primary concern. Unlike other theorists, however, Dharmakīrti advances a technical definition of “perception” as a cognition which is both nonconceptual and non-erroneous. Dharmakīrti’s definition of perception is thereby deliberately inclusive of three additional types of “perceptual” cognition, in (...) addition to veridical sensory awareness: the nonconceptual mental apprehension of an immediately-preceding cognition (“mental perception”), the vivid appearance of soteriologically efficacious objects of contemplative practice (“yogic perception”), and the sheer unmediated presence of the contents of cognition—whatever these might be—to the cognizing mind (“reflexive awareness”). Through the logical examination of what it means to be aware of an object, Dharmakīrti demonstrates that the awareness of an object is just the awareness of a phenomenal form or cognitive image produced by that object. Pursuing this analysis further, however, Dharmakīrti argues that the very notion of an object of cognition that exists “externally” or outside the mind is incoherent. Additionally, Dharmakīrti maintains that the phenomenological structure of subject and object—that is, the “first-personal” sense of one’s own cognitions as pertaining to oneself (“for-me-ness”), together with the inseparably concomitant sense that the objects of cognition exist “out there” in an extramental world—is strictly a form of cognitive error. Therefore, because ordinary sensory cognition is inherently structured by this subject-object duality, ordinary sensory cognition must in the final analysis be understood as erroneous. According to Dharmakīrti, in other words, ultimately only the nondual “luminosity” of reflexive awareness is genuinely perceptual, because only reflexive awareness is undistorted by nature. In this way, Dharmakīrti’s epistemology provides a theoretical foundation for the advanced nondual contemplative practices of Indian and Tibetan Buddhism, particularly Mahāmudrā and rDzogs chen. (shrink)

An increasing amount of twenty-first century metaphysics is couched in explicitly hyperintensional terms. A prerequisite of hyperintensional metaphysics is that reality itself be hyperintensional: at the metaphysical level, propositions, properties, operators, and other elements of the type hierarchy, must be more fine-grained than functions from possible worlds to extensions. In this paper I develop, in the setting of type theory, a general framework for reasoning about the granularity of propositions and properties. The theory takes as primitive the notion (...) of a substitution on a proposition (property, etc.) and, among other things, uses this idea to elucidate a number of theoretically important distinctions. A class of structures are identified which can be used to model a wide range of positions about the granularity of reality; certain of these structures are seen to receive a natural treatment in the category of M-sets. (shrink)

There is good reason to believe that scientific realism requires a commitment to the objective modal structure of the physical world. Causality, equilibrium, laws of nature, and probability all feature prominently in scientific theory and explanation, and each one is a modal notion. If we are committed to the content of our best scientific theories, we must accept the modal nature of the physical world. But what does the scientific realist’s commitment to physical modality require? We consider whether (...) scientific realism is compatible with Humeanism about the laws of nature, and we conclude that it is not. We specifically identify three major problems for the best-systems account of lawhood: its central concept of strength cannot be formulated non-circularly, it cannot offer a satisfactory account of the laws of the special sciences, and it can offer no explanation of the success of inductive inference. In addition, Humeanism fails to be naturalistically motivated. For these reasons, we conclude that the scientific realist must embrace natural necessity. (shrink)

The type-level abstraction is a formal way to represent molecular structures in biological practice. Graphical representations of molecular structures of biological objects are also used to identify functional processes of things. This paper will reveal that category theory is a formal mathematical language not only to visualize molecular structures of biological objects as type-level abstraction formally but also to understand how to infer biological functions from the molecular structures of biological objects. Category theory is a toolkit to understand (...) biological knowledge at the type-level formally, not individual token-level, as well as typical heuristic strategies in molecular biology. (shrink)

In this chapter I articulate and defend a basic principle capturing the underlying structure of an attractive sort of national reconciliation that accounts for a wide array of disparate judgments about the subject. There are extant theories of national reconciliation in the literature, most of which are informed by Kantian, liberal-democratic and similar perspectives. In contrast to these, I spell out a theory grounded on a comparatively underexplored sub-Saharan ethic. My foremost aim is to demonstrate how African ideals (...) about communal relationship, still largely unfamiliar to an international audience, do a promising job of providing a unified foundation for the roles of truth-telling, apology, forgiveness, compensation, amnesty and related practices often associated with national reconciliation. (shrink)